Thu., Oct. 04 notes

Our perception of cold
is more an indication of how quickly our body or hand is losing energy
than a reliable measurement of temperature.

Here's another example

It's pleasant standing outside on a nice day in 70 F air, it doesn't feel warm or cold. But if you jump into 70 F pool water you will feel cold, at least until you "get used to" the water temperature (your body might reduce blood flow to your extremities and skin to try to reduce energy loss).

Air is a poor conductor. If you go out in 40 F weather you will feel cold largely because there is a larger temperature difference between you and your surroundings (and temperature difference is one of the factors that affect rate of energy transport by conduction).

If you stick your hand into a bucket of 40 F water, it will feel very cold (your hand will actually soon begin to hurt). Keep some warm water nearby to warm up your hand.

Water is a much better conductor than air. Energy flows much more rapidly from your hand into the cold water. I mentioned in class that I thought this might be good for you. The reason is that successive application of hot and then cold is sometimes used to treat arthritis joint pain (it used to work wonders on my Dad's knee).

You can safely stick your hand into liquid nitrogen for a fraction of a second. There is an enormous temperature difference between your hand and the liquid nitrogen which would ordinarily cause energy to leave your hand at a dangerously high rate (which could cause your hand to freeze solid). It doesn't feel particularly cold though and doesn't feel wet. The reason is that some of the liquid nitrogen evaporates and quickly surrounds your hand with a layer of nitrogen gas. Just like air, nitrogen is a poor conductor (air is mostly nitrogen). The nitrogen gas insulates your hand from the cold for a very short time (the gas is a poor conductor but a conductor nonetheless). If you leave your hand in the liquid nitrogen for even a few seconds it would freeze. That would cause irreparable damage.

You can hold onto a Styrofoam cup of liquid nitrogen longer. That is because the air can't freely move; it's trapped in little air pockets in the foam. When air is free to move, convection will begin to transport energy at a more rapid rate than conduction alone.

A question came up in class a few semesters ago about sticking you hand (or maybe just the tip of one finger) into molten lead. I've never seen it done and certainly haven't tried it myself. But I suspected that you would first need to wet your hand. Then once you stick it into the lead the water would vaporize and surround your hand with a thin layer of gas, water vapor. The water vapor is a poor conductor just like the nitrogen and oxygen in air, and that protects your hand, for a short time, from the intense heat. Here's a video (and water does play a critical role)

Wind chill
Wind chill is a really good example of energy transport by convection. As a matter of fact I'm hoping that whenever you hear of energy transport by convection you'll first think of wind chill. Wind chill is also a reminder that our perception of cold is an indication of how quickly our body is losing energy rather than an accurate measurement of temperature.

Before we get into the details, here's a question:

It's 40 F outside,
the wind is blowing at 30 MPH,
and the wind chill temperature is 28 F.
What temperature would you measure with a thermometer?

Your body works hard to keep its core temperature around 98.6 F. If you go outside on a 40 F day (calm winds) you will feel cool; your body is losing energy to the colder surroundings (by conduction mainly). Your body will be able to keep you warm for a little while (perhaps indefinitely, I don't know). The 5 arrows represent the rate at which your body is losing energy.

A thermometer behaves differently, it is supposed to cool to the temperature of the surroundings. Once it reaches 40 F and has the same temperature as the air around it the energy loss will stop. If your body cools to 40 F you will die.

If you go outside on a 40 F day with 30 MPH winds your body will lose energy at a more rapid rate (because convection together with conduction are transporting energy away from your body). Note the additional arrows drawn on the figures above indicating the greater heat loss. This higher rate of energy loss will make it feel colder than a 40 F day with calm winds.

Actually, in terms of the rate at which your body loses energy, the windy 40 F day would feel the same as a 28 F day without any wind. Your body is losing energy at the same rate in both cases (9 arrows in both cases). The combination 40 F and 30 MPH winds results in a wind chill temperature of 28 F.

You would feel colder on a 40 F day with 30 MPH winds but the actual temperature is still 40 F. The thermometer will again cool to the temperature of its surroundings, it will just cool more quickly on a windy day. Once the thermometer reaches 40 F there won't be any additional energy flow or further cooling. The thermometer would measure 40 F on both the calm and the windy day.

Standing outside on a 40 F day is not an immediate life threatening situation. Falling into 40 F water is, you might last 30 minutes (though you might lose consciousness before that and die by drowning).

Energy will be conducted away from your body more quickly than your body can replace it. Your core body temperature will drop and bring on hypothermia.

Be sure not to confuse hypothermia with hyperthermia which can bring on heatstroke and is a serious outdoors risk in S. Arizona in the summer.

Talk of how long you would last in 40 F water reminds me of a page from the National Geographic Magazine that lists some of the limits of human survival. I'm trying to find a complete citation.

Latent heat energy transport involves changes in phase or state. You need to be able to add two types of information to this picture (this is p. 55 in the ClassNotes): (i) You should be able to name each of the phase changes shown above and (ii) You should also be able to indicate whether energy must be added to or removed from the material in order for each phase change to take place. And actually there is a third thing, (iii), that we'll get to in a minute.

A solid to liquid phase change is melting, liquid to gas is evaporation, and sublimation is a solid to gas phase change.

Dry ice is the best example of sublimation that I can think of. When placed in a warm room, dry ice turns directly from solid carbon dioxide to gaseous carbon dioxide without melting first. If you wash clothes and stick them outside on a dry cold (below freezing) day they will eventually dry. The clothes would first freeze but then the ice would slowly sublime away.

In each case above energy must be added to the material changing phase. You can consciously add or supply the energy (such as when you put water in a pan and put the pan on a hot stove and cause it to boil).

That much is pretty clear. The confusing part of this topic is when phase changes occur without you playing any role. Energy is still required to melt ice; in this case the needed energy will be taken from the surroundings. It is not always obvious what the "surroundings" are.

Here is the third thing to understand, (iii). When energy is taken from the surroundings, what effect will that have on the surroundings? When you take energy from the surroundings, the surroundings will cool.

Here's an example where you play the role of the surroundings. You'll be able to feel what happens when energy is taken from your body and used to evaporate some water.

When you step out of the shower in the morning you're covered with water. Some of the water evaporates. It doesn't ask permission, it just evaporates whether you want it to or not. The energy needed for evaporation is taken from the surroundings, from your body. Because your body is losing energy you feel cold.

The object of this figure is to give you some appreciation for the amount of energy involved in phase changes. A 240 pound man or woman running at 20 MPH has just enough kinetic energy (if you could capture it) to be able to melt an ordinary ice cube (I have been using Tedy Bruschi as an example for several years but he's now retired so I have switched to Scooby Wright). It would take 8 people running at 20 MPH to evaporate the resulting ice water.


Energy added to melt the ice is hidden in the water that results	Energy added to evaporate the water is added to the energy already in the water and is hidden in the water vapor

Again (i) try to name each phase change and (ii) show the direction of energy flow (into or out of the material) when the phase change occurs

You might not have heard of deposition before when a gas changes directly to a solid. The formation of frost is an example of deposition.

You can consciously remove energy from water vapor to make it condense. You take energy out of water to cause it to freeze (you could put water in a freezer; energy would flow from the relatively warm water to the colder surroundings). If one of these phase changes occurs, without you playing a role, energy will be released into the surroundings (causing the surroundings to warm).

Note the direction of the energy arrows - energy is being released into the surroundings (warming the surroundings). It's kind of like a genie coming out of a magic lamp. One Scooby Wright worth of kinetic energy is released when enough water freezes to make an ice cube. Many Scooby Wrights are released when water vapor condenses.

This release of energy into the surroundings and the warming of the surroundings is a little harder for us to appreciate because it never really happens to us in a way that we can feel. Have you ever stepped out of an air conditioned building into warm moist air outdoors and had your glasses or sunglasses "steam up"? Water vapor never condenses onto your body (your body is too warm). However if it did you would feel warm. It would be just the opposite of the cold feeling when you step out of the shower or a pool and the water on your body evaporates. You know how cold the evaporation can make you feel, the same amount of condensation would produce a lot of warming. I suspect we'd be surprised at how much warming it produces.

Alternate view showing the latent heat energy in water vapor and water coming out of hiding during a phase change and being released into the surroundings.

Here's a practical application of what we have been learning.

Cans of a cold drink are taken out of the refrigerator and placed on the kitchen table on a warm dry day and a warm humid day. Except for the differences in the amount of moisture in the air everything else is the same. Moisture has condensed onto the can above at right. Do the two cans warm up at the same rate or does one warm up more quickly than the other. In the latter case which can warms up most rapidly.

The can on the right will warm more quickly. Equal amounts of heat will flow from the warm air into the cold cans in both cases. Condensation of water vapor is an additional source of energy and will warm that can more rapidly. I suspect that the condensation may actually be the dominant process.

The foam "cozy", "koozie", or whatever you want to call it, that you can put around a can of soda or beer is designed to insulate the can from the warmer surroundings but also, and probably more importantly, to keep water vapor in the air from condensing onto the can (source of the image above)

We're beating this concept to death but we're almost done. Two more figures to illustrate how latent heat energy transport can carry energy from location to another. This first one is my favorite, it ties everything together.

1. You've just stepped out of the shower and are covered with water. The water is evaporating and energy is being taken from your body.

2. The water vapor (containing the energy taken from your body), drifts into the kitchen where it finds a cold can sitting on a table.

3. Water vapor comes into contact with the cold can and condenses. The hidden latent heat energy in the water vapor is released into the can and warms the drink inside.

Without you even leaving the bathroom,
energy has effectively been transported from your warm body to the cold can in the kitchen.

Here's what happens on a much grander scale in the atmosphere.

Energy transport by electromagnetic radiation
It's time to tackle electromagnetic (EM) radiation, the 4th and most important of the energy transport processes (it's the most important because it can transport energy through empty space (outer space)).

Many introductory textbooks depict EM radiation with a wavy line like shown above. They don't usually explain what the wavy line represents.

An electric field arrow (vector)
just shows the direction and
gives you an idea of the strength
of the electrical force
that would be exerted on a positive charge at that position.

We imagine turning on a source of EM radiation and then a very short time later we take a snapshot. In that time the EM radiation has traveled to the right (at the speed of light). The EM radiation is a wavy pattern of electric and magnetic field arrows. We'll ignore the magnetic field arrows. The E field arrows sometimes point up, sometimes down. The pattern of electric field arrows repeats itself.

Note the + charge near the right side of the picture. At the time this picture was taken the electric field at the position of the + charge points upward. There is a fairly strong upward pointing force being exerted on the + charge.

This picture above was taken a short time after the first snapshot after the radiation had traveled a little further to the right. The EM radiation now exerts a somewhat weaker downward force on the + charge.

A 3rd snapshot taken a short time later. The + charge is now being pushed upward again.
A movie of the + charge, rather than just a series of snapshots, would show the charge bobbing up and down much like a swimmer in the ocean would do as waves passed by.

I doubt if we go past this point on Thursday.

Wavelength and frequency
The wavy pattern used to depict EM radiation can be described spatially (what you would see in a snapshot) in terms of its wavelength, the distance between identical points on the pattern.

Or you can describe the radiation temporally using the frequency of oscillation (number of up and down cycles completed by an oscillating charge per second). By temporally we mean you look at one particular fixed point and look at how things change with time.

You add energy when you cause an electrical charge to move up and down and create the EM radiation (top left).

In the middle figure, the EM radiation that is produced then travels out to the right (it could be through empty space or through something like the atmosphere).